Late-season twisters hit Oklahoma and Oregon as well.
Luke and Cindy McKittrick were killed Thursday evening when the storm hit Texas' Wise County. Their 20-month-old granddaughter, Kylie, was hospitalized in good condition. Two other people were in critical condition and one was in good condition. The fifth injured person was not hospitalized.
Chico is about about 50 miles north of Fort Worth.
The severe weather, associated with a cold front, produced high winds, downpours and quarter-sized hail, authorities said.
Wise County Sheriff's Department and emergency officials say witnesses saw rotational winds indicating the damage was caused by a tornado.
But the National Weather Service has not determined whether down-burst winds or a tornado was to blame, meteorologist Jesse Moore said.
The National Weather Service was sending investigators to determine whether the damage was caused by thunderstorm winds or a tornado, said Gifford Ely, meteorologist at the National Weather Service in Fort Worth.
"The way the damage has been described, it would not surprise me if a short-lived tornado came out of that storm," Ely said.
In Oklahoma, a series of spring-like storms Thursday produced high winds, hail and tornadoes that damaged homes and other structures and toppled power lines across the state.
A tornado damaged 10 homes in a 3-mile path through Noble County in central Oklahoma, authorities said. A second tornado was also spotted in the county but was not believed to have caused much damage.
Tornado warnings also were issued for Logan County in Guthrie and Mulhall, areas hit May 3 by powerful twisters that killed 44 and left thousands homeless.
Geary police Officer Ricky Ambrose said as many as four houses were damaged by a tornado on the western edge of Guthrie. No serious injuries were reported.
In Creswell, Ore., 10 miles south of Eugene, a tornado touched down Tuesday afternoon near an elementary school, causing minor damage to a few homes and businesses. There were no reports of injuries.